Ray Optics · JEE Main previous year questions

A prism of angle $75^{\circ }$ and refractive index $\sqrt{3}$ is coated with thin film of refractive index 1.5 only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be _____ $(\sin 15^{\circ }=0.25\text{ and }\sin 25^{\circ }=0.43)$

1. A.between $15^{\circ }$ and $20^{\circ }$
2. B.$15^{\circ }$
3. C.$<15^{\circ }$
4. D.$>25^{\circ }$

The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is _____ cm.

A thin convex lens of focal length 5 cm and a thin concave lens of focal length 4 cm are combined together (without any gap) and this combination has magnification $m_1$ when an object is placed 10 cm before the convex lens. Keeping the positions of convex lens and object undisturbed a gap of 1 cm is introduced between the lenses by moving the concave lens away, which lead to a change in magnification of total lens system to $m_2$. The value of $\left|\frac{m_1}{m_2}\right|$ is ____.

1. A.$\frac{25}{27}$
2. B.$\frac{5}{6}$
3. C.$\frac{5}{27}$
4. D.$\frac{3}{2}$

Consider an equilateral prism (refractive index $\sqrt{2}$). A ray of light is incident on its one surface at a certain angle $i$. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to ____

1. A.$30^{\circ }$
2. B.$20^{\circ }$
3. C.$40^{\circ }$
4. D.$15^{\circ }$

A parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius of curvature 50 cm . Refractive index of glass is 1.5 . The rays converge to a point at a distance $x\mathrm{cm}$ from the centre of the curvature of the spherical surface. The value of $x$ is ____ cm .

In a microscope the objective is having focal length $f_o=2\mathrm{cm}$ and eye-piece is having focal length $f_e=4\mathrm{cm}$. The tube length is 32 cm . The magnification produced by this microscope for normal adjustment is ____.

A collimated beam of light of diameter 2 mm is propagating along $x$-axis. The beam is required to be expanded in a collimated beam of diameter 14 mm using a system of two convex lenses. If first lens has focal length 40 mm , then the focal length of second lens is ____ mm.

1. A.$75^{\circ }$
2. B.$90^{\circ }$
3. C.$60^{\circ }$
4. D.$45^{\circ }$

A convex lens of focal length $30\mathrm{cm}$ is placed in contact with a concave lens of focal length $20\mathrm{cm}$. An object is placed at $20\mathrm{cm}$ to the left of this lens system. The distance of the image from the lens in $\mathrm{cm}$ is $\underline{}$.

1. A.$\frac{60}{7}$
2. B.$15$
3. C.$45$
4. D.$30$

A concave-convex lens of refractive index $1.5$ and the radii of curvature of its surfaces are $30\mathrm{cm}$ and $20\mathrm{cm}$, respectively. The concave surface is upwards and is filled with a liquid of refractive index $1.3$. The focal length of the liquid-glass combination will be

1. A.$\frac{700}{11}\mathrm{cm}$
2. B.$\frac{600}{11}\mathrm{cm}$
3. C.$\frac{800}{11}\mathrm{cm}$
4. D.$\frac{500}{11}\mathrm{cm}$

When an object is placed 40 cm away from a spherical mirror an image of magnification $\frac{1}{2}$ is produced. To obtain an image with magnification of $\frac{1}{3}$, the object is to be moved :

1. A.20 cm away from the mirror.
2. B.20 cm towards the mirror.
3. C.80 cm away from the mirror.
4. D.40 cm away from the mirror.

A small mirror of mass $m$ is suspended by a massless thread of length $l$. Then the small angle through which the thread will be deflected when a short pulse of laser of energy E falls normal on the mirror ($c=\text{speed of light in vacuum}$ and $g=\text{acceleration due to gravity}$)

1. A.$\theta =\frac{E}{mc\sqrt{gl}}$
2. B.$\theta =\frac{E}{2mc\sqrt{gl}}$
3. C.$\theta =\frac{3E}{4mc\sqrt{gl}}$
4. D.$\theta =\frac{2E}{mc\sqrt{gl}}$

Distance between object and its image (magnified by $-\frac{1}{3}$ ) is 30 cm . The focal length of the mirror used is $(\frac{x}{4})\mathrm{cm}$, where magnitude of value of $x$ is ____.

A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm . A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is :

1. A.45 cm
2. B.15 cm
3. C.22.5 cm
4. D.7.5 cm

Consider following statements for refraction of light through prism, when angle of deviation is minimum. A. The refracted ray inside prism becomes parallel to the base. B. Larger angle prisms provide smaller angle of minimum deviation. C. Angle of incidence and angle of emergence becomes equal. D. There are always two sets of angle of incidence for which deviation will be same except at minimum deviation setting. E. Angle of refraction becomes double of prism angle. Choose the correct answer from the options given below :

1. A.A, B and E Only
2. B.B, C and D Only
3. C.B, D and E Only
4. D.A, C and D Only

The radii of curvature for a thin convex lens are 10 cm and 15 cm respectively. The focal length of the lens is 12 cm . The refractive index of the lens material is

1. A.1.4
2. B.1.8
3. C.1.5
4. D.1.2

A monochromatic light of frequency $5\times 10^{14}\mathrm{Hz}$ travelling through air, is incident on a medium of refractive index ' 2 '. Wavelength of the refracted light will be :

1. A.$400\mathrm{nm}$
2. B.$300\mathrm{nm}$
3. C.$600\mathrm{nm}$
4. D.$500\mathrm{nm}$

Light from a point source in air falls on a spherical glass surface (refractive index, $\mu =1.5$ and radius of curvature $=50\mathrm{cm}$). The image is formed at a distance of $200\mathrm{cm}$ from the glass surface inside the glass. The magnitude of distance of the light source from the glass surface is __________$\mathrm{m}$.

1. A.0.24 m left to the spherical surface
2. B.0.24 m right to the spherical surface
3. C.0.4 m left to the spherical surface
4. D.0.4 m right to the spherical surface

1. A.$-\alpha$
2. B.$-\frac{\alpha }{2}$
3. C.$-45^{\circ }$
4. D.$+45^{\circ }$

Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of $12\mathrm{cm}$ , at same distance of $18\mathrm{cm}$ from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is :

1. A.2
2. B.$1/2$
3. C.$1/3$
4. D.3

A bi-convex lens has radius of curvature of both the surfaces same as $1/6\mathrm{cm}$. If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides $(R_1\ne R_2)$, without any change in lens power then possible combination of $R_1$ and $R_2$ is :

1. A.$\frac{1}{3}\mathrm{cm}$ and $\frac{1}{7}\mathrm{cm}$
2. B.$\frac{1}{5}\mathrm{cm}$ and $\frac{1}{7}\mathrm{cm}$
3. C.$\frac{1}{3}\mathrm{cm}$ and $\frac{1}{3}\mathrm{cm}$
4. D.$\frac{1}{6}\mathrm{cm}$ and $\frac{1}{9}\mathrm{cm}$

A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to $60^{\circ }$. The refractive index of the prism material is $\sqrt{2}$. The angle of incidence (in degrees) is ____.

A convex lens made of glass (refractive index = 1.5) has focal length 24 cm in air. When it is totally immersed in water (refractive index = 1.33), its focal length changes to

1. A.96 cm
2. B.72 cm
3. C.24 cm
4. D.48 cm

1. A.$0.124\mathrm{R}$
2. B.$0.114\mathrm{R}$
3. C.$0.411\mathrm{R}$
4. D.$0.214\mathrm{R}$